Negative Quasi-Probability as a Resource for Quantum Computation

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analog of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic-state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.Comment: 15 pages v4: This is a major revision. In particular, we have added a new section detailing an explicit extension of the Gottesman-Knill simulation protocol to deal with positively represented states and measurement (even when these are non-stabilizer). This paper also includes significant elaboration on the two main results of the previous versio

Long-term adherence to healthy dietary guidelines and chronic inflammation in the prospective Whitehall II study

Background Inflammation plays an important role in the cause of cardiovascular diseases and may contribute to the association linking an unhealthy diet to chronic age-related diseases. However, to date the long-term associations between diet and inflammation have been poorly described. Our aim was to assess the extent to which adherence to a healthy diet and dietary improvements over a 6-year exposure period prevented subsequent chronic inflammation over a 5-year follow-up in a large British population of men and women. Methods Data were drawn from 4600 adults (mean ± standard deviation, age 49.6 ± 6.1 years, 28% were women) from the prospective Whitehall cohort II study. Adherence to a healthy diet was measured using Alternative Healthy Eating Index (AHEI) scores in 1991-1993 (50.7 ± 11.9 points) and 1997-1999 (51.6 ± 12.4 points). Chronic inflammation, defined as average levels of serum interleukin-6 from 2 measures 5 years apart, was assessed in 1997-1999 and 2002-2004. Results After adjustment for sociodemographic factors, health behaviors, and health status, participants who maintained a high AHEI score (ie, a healthy diet, n = 1736, 37.7%) and those who improved this score over time (n = 681, 14.8%) showed significantly lower mean levels of interleukin-6 (1.84 pg/mL, 95% confidence interval [CI], 1.71-1.98 and 1.84 pg/mL, 95% CI, 1.70-1.99, respectively) than those who had a low AHEI score (n = 1594, 34.6%) over the 6-year exposure period (2.01 pg/mL, 95% CI, 1.87-2.17). Conclusions These data suggest that maintaining and improving adherence to healthy dietary recommendations may reduce the risk of long-term inflammation.</p

Gender-specific associations of short sleep duration with prevalent and incident hypertension : the Whitehall II Study

Sleep deprivation (5 hour per night) was associated with a higher risk of hypertension in middle-aged American adults but not among older individuals. However, the outcome was based on self-reported diagnosis of incident hypertension, and no gender-specific analyses were included. We examined cross-sectional and prospective associations of sleep duration with prevalent and incident hypertension in a cohort of 10 308 British civil servants aged 35 to 55 years at baseline (phase 1: 1985-1988). Data were gathered from phase 5 (1997-1999) and phase 7 (2003-2004). Sleep duration and other covariates were assessed at phase 5. At both examinations, hypertension was defined as blood pressure 140/90 mm Hg or regular use of antihypertensive medications. In cross-sectional analyses at phase 5 (n5766), short duration of sleep (5 hour per night) was associated with higher risk of hypertension compared with the group sleeping 7 hours, among women (odds ratio: 2.01; 95% CI: 1.13 to 3.58), independent of confounders, with an inverse linear trend across decreasing hours of sleep (P0.003). No association was detected in men. In prospective analyses (mean follow-up: 5 years), the cumulative incidence of hypertension was 20.0% (n740) among 3691 normotensive individuals at phase 5. In women, short duration of sleep was associated with a higher risk of hypertension in a reduced model (age and employment) (6 hours per night: odds ratio: 1.56 [95% CI: 1.07 to 2.27]; 5 hour per night: odds ratio: 1.94 [95% CI: 1.08 to 3.50] versus 7 hours). The associations were attenuated after accounting for cardiovascular risk factors and psychiatric comorbidities (odds ratio: 1.42 [95% CI: 0.94 to 2.16]; odds ratio: 1.31 [95% CI: 0.65 to 2.63], respectively). Sleep deprivation may produce detrimental cardiovascular effects among women. (Hypertension. 2007;50:694-701.) Key Words: sleep duration blood pressure hypertension gender differences confounders comorbiditie

Change in Sleep Duration and Type 2 Diabetes: The Whitehall II Study

OBJECTIVE Evidence suggests that short and long sleep durations are associated with a higher risk of type 2 diabetes. Using successive data waves spanning &amp;gt;20 years, we examined whether a change in sleep duration is associated with incident diabetes. RESEARCH DESIGN AND METHODS Sleep duration was reported at the beginning and end of four 5-year cycles: 1985–1988 to 1991–1994 (n = 5,613), 1991–1994 to 1997–1999 (n = 4,193), 1997–1999 to 2002–2004 (n = 3,840), and 2002–2004 to 2007–2009 (n = 4,195). At each cycle, change in sleep duration was calculated for participants without diabetes. Incident diabetes at the end of the subsequent 5-year period was defined using 1) fasting glucose, 2) 75-g oral glucose tolerance test, and 3) glycated hemoglobin, in conjunction with diabetes medication and self-reported doctor diagnosis. RESULTS Compared with the reference group of persistent 7-h sleepers, an increase of ≥2 h sleep per night was associated with a higher risk of incident diabetes (odds ratio 1.65 [95% CI 1.15, 2.37]) in analyses adjusted for age, sex, employment grade, and ethnic group. This association was partially attenuated by adjustment for BMI and change in weight (1.50 [1.04, 2.16]). An increased risk of incident diabetes was also seen in persistent short sleepers (average ≤5.5 h/night; 1.35 [1.04, 1.76]), but this evidence weakened on adjustment for BMI and change in weight (1.25 [0.96, 1.63]). CONCLUSIONS This study suggests that individuals whose sleep duration increases are at an increased risk of type 2 diabetes. Greater weight and weight gain in this group partly explain the association. </jats:sec

Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

Changes Over Time in Absolute and Relative Socioeconomic Differences in Smoking: A Comparison of Cohort Studies From Britain, Finland, and Japan

INTRODUCTION: Socioeconomic differences in smoking over time and across national contexts are poorly understood. We assessed the magnitude of relative and absolute social class differences in smoking in cohorts from Britain, Finland and Japan over 5-7 years. METHODS: The British Whitehall II study (n=4350), Finnish Helsinki Health Study (n=6328), and Japanese Civil Servants Study (n=1993) all included employed men and women aged 35-68 at baseline in 1997-2002. Follow-up was in 2003-2007 (mean follow-up 5.1, 6.5 and 3.6 years, respectively). Occupational social class (managers, professionals and clerical employees) was measured at baseline. Current smoking and covariates (age, marital status, body mass index and self-rated health) were measured at baseline and follow-up. We assessed relative social class differences using the Relative Index of Inequality (RII) and absolute differences using the Slope Index of Inequality (SII). RESULTS: Social class differences in smoking were found in Britain and Finland, but not in Japan. Age-adjusted relative differences at baseline ranged from RII 3.08 (95% confidence interval 1.99-4.78) among Finnish men to 2.32 (1.24-4.32) among British women, with differences at follow-up greater by 8-58%. Absolute differences remained stable and varied from SII 0.27 (0.15-0.40) among Finnish men to 0.10 (0.03-0.16) among British women. Further adjustment for covariates had modest effects on inequality indices. CONCLUSIONS: Large social class differences in smoking persisted among British and Finnish men and women, with widening tendencies in relative differences over time. No differences could be confirmed among Japanese men or women

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

Overall Diet History and Reversibility of the Metabolic Syndrome Over 5 Years: The Whitehall II prospective cohort study

International audienceOur findings support the benefit of adherence to AHEI dietary guidelines for individuals with MetS, especially those with central obesity or high triglyceride levels